×

Mixed Jacobi-like forms of several variables. (English) Zbl 1215.11051

The author studies mixed Jacobi-like forms of several variables associated to equivariant maps of the Poincaré upper-half plane in connection with usual Jacobi-like forms, Hilbert modular forms. The author constructs a lifting of a mixed automorphic forms to such a mixed Jacobi-like form. The author also gives some applications and examples related to the mixed Jacobi-like forms.

MSC:

11F50 Jacobi forms
32N10 Automorphic forms in several complex variables
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Cohen, P. B.; Manin, Y.; Zagier, D., Automorphic pseudodifferential operators, Algebraic Aspects of Integrable Systems. Algebraic Aspects of Integrable Systems, Progress in Nonlinear Differential Equations and Their Applications, 26, 17-47 (1997), Massachusetts: Birkhäuser Boston, Massachusetts · Zbl 1055.11514
[2] Dong, C.; Mason, G., Transformation laws for theta functions, Proceedings on Moonshine and Related Topics (Montréal, QC, 1999), American Mathematical Society · Zbl 1002.11038
[3] Freitag, E., Hilbert Modular Forms, viii+250 (1990), Berlin: Springer, Berlin · Zbl 0702.11029
[4] Garrett, P. B., Holomorphic Hilbert Modular Forms. Holomorphic Hilbert Modular Forms, The Wadsworth & Brooks/Cole Mathematics Series, xvi+304 (1990), California: Wadsworth, California · Zbl 0685.10021
[5] Kodaira, K., On compact analytic surfaces. II, Annals of Mathematics. Second Series, 77, 563-626 (1963) · Zbl 0118.15802
[6] Lee, M. H., Mixed cusp forms and holomorphic forms on elliptic varieties, Pacific Journal of Mathematics, 132, 2, 363-370 (1988) · Zbl 0648.14017
[7] Lee, M. H., Mixed Jacobi-like forms, Complex Variables. Theory and Application, 42, 4, 387-396 (2000) · Zbl 1045.11026
[8] Lee, M. H., Hilbert modular pseudodifferential operators, Proceedings of the American Mathematical Society, 129, 11, 3151-3160 (2001) · Zbl 0986.11030 · doi:10.1090/S0002-9939-01-06117-2
[9] Lee, M. H., Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms. Mixed Automorphic Forms, Torus Bundles, and Jacobi Forms, Lecture Notes in Mathematics, 1845, x+239 (2004), Berlin: Springer, Berlin · Zbl 1063.11012
[10] Miyamoto, M., A modular invariance on the theta functions defined on vertex operator algebras, Duke Mathematical Journal, 101, 2, 221-236 (2000) · Zbl 0988.17021 · doi:10.1215/S0012-7094-00-10123-8
[11] Stiller, P., Special values of Dirichlet series, monodromy, and the periods of automorphic forms, Memoirs of the American Mathematical Society, 49, 299, iv+116 (1984) · Zbl 0536.10023
[12] Zagier, D., Modular forms and differential operators, Proceedings of the Indian Academy of Sciences. Mathematical Sciences, 104, 1, 57-75 (1994) · Zbl 0806.11022
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.